Bring a large, deep pot of salted water to a gentle boil and add vegetable oil.

Fill wonton wrappers with 1 teaspoons edamame filling and top filling with a cilantro leaf (cover unfilled wrappers with a moist towel). Moisten wrapper edges with water, fold over filling, and press to seal. Boil wontons in batches until they float to surface, 2 minutes. Serve with soy sauce.